Can a program that requires feedback be considered an AI?
There is no "process of AI" as such.  There are many, many different approaches to AI, different ones of which are used in specific applications.  

As to whether a purely trial and error approach could be considered AI... I'd offer up a qualified "maybe".  If you do nothing but an exhaustive scan of the solution space, for every trial, then I'd say "No, it's not really any kind of AI".  OTOH, if you're using a knowledge-base of some sort and applying some kind of reasoning (even if it's a heuristic) , and if you have a system that somehow learns from the feedback from the user and gets "smarter" over time, then you're likely working on something that could be considered AI.   

All of that said, the exact definition of what is and isn't AI is somewhat fuzzy.   One popular definition is something like "any technology that allows a computer to do something well that currently only humans can do well". So if you're doing something that fits that descriptions, it's possibly an aspect of AI.   And consider again that most people don't really consider "brute force" solutions to be AI.